As described in U.S. Pat. No. 6,747,915, a seismic image of an earth formation can be obtained using at least one seismic source and at least one seismic receiver. The source generates a seismic wave into the earth formation, in which formation the seismic wave is reflected by acoustic-impedance contrasts and refracted through media having a variable velocity. The reflected wave is received by the seismic receiver(s). A receiver detects the reflected wave and records it in the form of a signal or seismic trace. The receivers record one signal per receiver and the signals or traces are compiled to yield the seismic image of the underground formation.
In order to avoid the need to place seismic sources in the formation, the '915 patent discloses using an array of sources at the surface in conjunction with multiple receivers in the formation and manipulating the signals in such a way that it appears as if the seismic waves originate from a source at the location of a selected receiver. Such a source is called a virtual source, to distinguish it from a real source, which can be located at the other side of a complex transmission medium i.e. the intervening formation.
It has been found, however, in practice, because there is only finite number of sources, inhomogeneous radiation of the virtual sources results in incorrect measurement of the signal amplitudes. Thus, it is desirable to provide a technique that is capable of providing true-amplitude imaging in a virtual source context, even in inhomogeneous media.